IntroductionI. General Properties of PolynomialsII. General Properties of EquationsIII. Relations Between the Roots and Coefficients of Equations, with Applications to Symmetric Functions of the RootsIV. Transformation of EquationsV. Solution of Reciprocal and Binomial EquationsVI. Algebraic Solution of the Cubic and BiqudaraticVII. Properties of the Derived FunctionsVIII. Symmetric Functions of the RootsIX. Limits of the Roots of EquationsX. Separation of the Roots of EquationsIX. Solution of Numerical EquationsXII. Complex Numbers and the Complex VariableNotesXIII. DeterminantsXIC. EliminationXV. Calculation of Symmetric Functions-Seminvariants and SemicovariantsXVI. Covariants and InvariantsXVII. Covariants and Invariants of the Quadratic, Cubic, and QuarticXVIII. Covariants and Invariants of Combined FormsXIX. TransformationsXX. Theory of Substitutions and GroupsNotes